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Extra resources for Advanced Computational Methods in Science and Engineering

Sample text

This is due to the imaginary term, β2 i in the shifted Laplacian. LFA also indicates that Mh based on the fourth-order discretization can be dealt with in multigrid as efficiently as the second-order discretization. 4, and obtain an efficient preconditioned Krylov subspace method. 5). 5 was chosen for the high wavenumber problems. The other multigrid components were: • Restriction operators, IhH , based on 2D full weighting, whose stencil [54] reads: H 121 ∧ 1  2 4 2 , IhH = 16 121 h  (11) with h denoting the fine-, and H denoting the coarse-mesh size.

E. Plessix van Gijzen for their input in the project. P. MacLachlan and N. Umetani for their contribution to this article, as the present article relies on paper [57] of which they are the co-authors. N. Umetani performed some additional numerical experiments, especially for this paper. References 1. T. A IRAKSINEN , E. H EIKKOLA , A. P ENNANEN , J. T OIVANEN , An algebraic multigrid based shifted-Laplacian preconditioner for the Helmholtz equation. J. Comp. Physics, 226: 1196–1210, 2007. 2. R.